/home/nowonder/forschung/aprove/TPDB05/TRS/TRCSR/Ex26_Luc03b_FR.trs

The program

(VAR N X Y Z X1 X2)
(RULES 
terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
sqr(0) -> 0
sqr(s(X)) -> s(n__add(n__sqr(activate(X)),n__dbl(activate(X))))
dbl(0) -> 0
dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
add(0,X) -> X
add(s(X),Y) -> s(n__add(activate(X),Y))
first(0,X) -> nil
first(s(X),cons(Y,Z)) -> cons(Y,n__first(activate(X),activate(Z)))
terms(X) -> n__terms(X)
s(X) -> n__s(X)
add(X1,X2) -> n__add(X1,X2)
sqr(X) -> n__sqr(X)
dbl(X) -> n__dbl(X)
first(X1,X2) -> n__first(X1,X2)
activate(n__terms(X)) -> terms(activate(X))
activate(n__s(X)) -> s(X)
activate(n__add(X1,X2)) -> add(activate(X1),activate(X2))
activate(n__sqr(X)) -> sqr(activate(X))
activate(n__dbl(X)) -> dbl(activate(X))
activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
activate(X) -> X
)

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